Department of

Mathematics


Seminar Calendar
for events the day of Friday, March 7, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, March 7, 2014

1:00 pm in 341 Altgeld Hall,Friday, March 7, 2014

Immersions into Robertson-Walker spacetimes

Marie-Amelie Lawn (U Texas )

Abstract: Robertson-Walker spacetimes are special cases of pseudo-Riemannian warped products which arise as exact solutions of the Einstein field equations in general relativity. We will consider hypersurfaces of such spaces and give a necessary and su?cient condition for a Riemannian manifold to locally isometrically immerse into them. If we have more time, we will speak about generalized associated families of surface immersions into 3D Robertson-Walker and homogeneous spaces.

3:00 pm in 343 Altgeld Hall,Friday, March 7, 2014

Zeros of characters for the symmetric group

Alexander Miller (University of Minnesota)

Abstract: Let X be chosen at random from the irreducible characters of the symmetric group of degree n and let g be chosen at random from the group itself. What is the probability that X(g) equals 0? We show that the probability tends to 1 as n tends to infinity and discuss some natural variations of the question.

3:00 pm in 243 Altgeld Hall,Friday, March 7, 2014

Brought to you by the letter B

Sarah Yeakel (UIUC Math)

Abstract: Topologists tend to hide a lot of machinery in notation. One goal of this talk is to motivate the use of the letter B for classifying spaces of principal bundles in view of the algebraic bar construction (also denoted with a B). We'll spend the rest of the talk basking in the beauty and bearings of the brazenly beneficial bar construction.

4:00 pm in 347 Altgeld Hall,Friday, March 7, 2014

Symplectic resolutions, hypertoric varieties, and special polynomials

Travis Schedler (University of Texas-Austin)

Abstract: Hypertoric varieties are the symplectic analogue of toric varieties, obtained by Hamiltonian reduction of a symplectic vector space by a torus. The resulting cone is singular, but under mild conditions admits a symplectic resolution of singularities. With Etingof I have defined a new cohomology theory, Poisson-de Rham cohomology, which conjecturally recovers the de Rham cohomology of the resolution. I will prove this conjecture in the hypertoric case, via joint work with Proudfoot. Moreover this cohomology theory comes with an extra weight grading, which we show recovers a variant of the Tutte polynomial of the associated hyperplane arrangement. The arguments apply to general symplectic varieties; in the case of slices to nilpotent coadjoint orbit closures for semisimple Lie groups, we recover Kostka polynomials. The talk will not require prior familiarity with any of the mentioned topics.

4:00 pm in 345 Altgeld Hall,Friday, March 7, 2014

Embedding E_0

Slawomir Solecki (UIUC Math)

Abstract: We will read the paper ``An embedding theorem of E_0 with model theoretic applications" by Kaplan and Miller (http://arxiv.org/pdf/1308.5515v1.pdf)